Ch 18: Modelling Flashcards
What is a model?
A model can be defined as a ‘cat-down, simplified version of reality that captures the essence of a problem and aids understanding.
It is important to be able to communicate the results of the model effectively and clearly.
Modelling requires a balance to be struck between which two things?
1) Reality, and hence complexity
2) Simplicity, for ease of use, verification and interpretation of results.
What is the advantage of an actuarial model over a formula?
A model is better able to reflect uncertain future events by giving an indication of the effects of varying the assumptions.
This is important so that the client understands the uncertainty involved in the underlying assumptions.
Where might a model come from and what factors affect the decision about where to get it?
1) A model might be developed in-house
2) An existing model may be modified
3) A commercial model might be purchased externally
4) The factors that need to be considered are:
- Fit for purpose
- Expertise available in-house
- Need for flexibility
- Cost of each option
- Expected number of times the model is to be used
- Desired level of accuracy
- Cost to make the model
- Cost to run the model
Outline the operational issues that need to be considered when designing and constructing a model
SCARCER FILES
- Simple, but retains key features
- Clear results
- Adequately documented
- Range of implementation methods
- Communicable workings and output
- Easy to understand
- Refinable and developable
- Frequency of cashflows (balance accuracy vs practicality)
- Independent verification of outputs
- Length of run not too long
- Expenses not too high
- Sensible joint behavior of variables
Define what is meant by ‘dynamism’ of a model
If a model is dynamic, then the assets and liability parts of the model and all the assumptions are consistent with each other and are programmed to interact under different scenarios as they do in reality
For example:
- Inflation rates and investment returns
- Bonus rates and investment returns
- Withdrawal rates and economic conditions
Set out steps involved in developing and running a deterministic model
1) Specify the purpose of the investigation
2) Collect, group and modify data
3) Choose the form of the model and its parameters/variables
4) Ascribe values to those parameters using past experience/estimations
5) Construct the model based on expected cashflows
6) Test the model and correct if necessary
7) Check the goodness of fit using past data, modify if poor.
8) Run using estimates of future values of variables
9) Sensitivity tests (and maybe scenario test) using different parameter values.
Additional/Alternative steps in a stochastic model
1) Choose s density function for each of the stochastic variables
2) Specify the correlations between the variables
3) Run model many times using a random sample from the chosen density function
4) Produce a summary of results - a distribution (e.g. summarized at various confidence levels)
Outline the two factors to consider in choosing the time period (or frequency) for the projection of cashflows in a model
1) The more frequently the cashflows are calculated, the more reliable the output from the model, although there is a danger of spurious accuracy.
2) The less frequently the cashflows are calculated, the faster the model can be run, and the results obtained.
What are the relative merits of deterministic vs stochastic models?
Deterministic:
- Quicker, cheaper and easier to design, build and run.
- Clearer what scenarios have been tested.
- Results are easier to explain to a non-technical audience.
Stochastic:
- Allows naturally for the uncertainty of outcomes
- Enables better modelling of the correlations between variables
- Test a wider range of scenarios
- Good at identifying extreme outcomes, which may not have been thought of under a deterministic scenario.
- Important in assessing the impact of financial guarantees
Outline how a deterministic model could be used to determine a set of new premium rates for a term assurance contract.
1) An objective would be set based on profit criterion and an appropriate time horizon.
2) Data relating to the existing profile of customers would be collected and model points created. It would be modified for any perceived future differences in the profile of customers.
3) Parameter values for key assumptions such as mortality, expenses, lapses and investment returns would be set based on past experience.
4) For each model point, the model would be run, projecting future cashflows and discounting the net profits at the risk discount rate (RDR). The premium would be varied until the required profit criterion is met.
List 4 methods of assessing statistical risk
1) Analytically - by considering the variances of the individual parameter values used.
2) By using sensitivity analysis, with deterministically assessing variations in parameter values.
3) By using stochastic models for some, or all, of the parameter values and simulations.
4) By comparison with the available market data.
What should the rate used to discount the net cashflows in the model reflect?
1) The return required by the company
2) The level of statistical risk attaching to the cashflows.
Note: In theory, a different discount rate should be used for each cashflow (as the risk is different); In practice, a single rate is often used based on the average risk of the product.
What are model points? Why are they used?
How may they be chosen?
A model point is a representative single policy.
The business being modelled may comprise a very large number of different policies and it may be too time consuming to run all of these through a model.
So policies are classified into relatively homogeneous groups.
A model point for each group is chosen that is representative of the whole group.
The model point is run through the model and the output is then scaled up by the number of policies in the group to give the results of the whole group.
For pricing purposes, model points are chosen to reflect the expected profile of future business to be sold. This could be based on the existing profile, or that of a similar product.
When are model point not used?
Model points are not generally used when valuing liabilities for calculating reserves.
The normal procedure for determining the value of life assurance or pension scheme liabilities is to value the benefits for each policy or scheme individually.
In many territories, this may be a regulatory requirement.
However, model points may be required in order to answer various ‘what if’ questions.
